Math, asked by aswanthsukumar36211, 11 months ago

ABC is a triangle whose area is 50 cm square . Eand F are are midpoints of the sides.AB and AC respectively . Prove that EBCF is a trapezium and find its area

Answers

Answered by amitnrw
1

Area of EBCF trapezium =   37.5 cm²

Step-by-step explanation:

E  & F  are mid points of AB & AC

=> AE = BE  = AB/2    & AF = CF = AC/2

=> BE/AB = 1/2  = CF/AC

Lets draw AD ⊥ BC , EM ⊥BC  & FN⊥BC

Now in

Δ BEM & Δ BAD

∠B = ∠B ( common)

∠BME = ∠BDA = 90°

=> Δ BEM ≈ Δ BAD

=> BE/AB  = EM/AD

Simialrly

Δ CFN ≈ Δ CAD

=> CF/AC = FN/AD

BE/AB = 1/2  = CF/AC

=> EM/AD = FN/AD

=> EM = FN

EM = FN  ( EM & FN are perpincular to BC   from EF)

=> EF ║BC

Hence EBCF is a trazpezium

ΔAEF ≈ ABC

ar (ΔAEF) / ar (ΔABC)  = (AE/AB)² = 1/4

ar (ΔAEF) = 50/4

Area of EBCF trapezium =  ar (ΔABC) - ar (ΔAEF)  = 50 - 50/4

= 150/4

= 37.5 cm²

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